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Title: Plane shearing waves of arbitrary form: Exact solutions of the Navier-Stokes equations.
Authors: Singh, Nishant K.
Sridhar, S.
Issue Date: Sep-2017
Publisher: Springer Verlag
Citation: European Physical Journal Plus, 2017, Vol. 132, p 403
Abstract: We present exact solutions of the incompressible Navier-Stokes equations in a background linear shear flow. The method of construction is based on Kelvin’s investigations into linearized disturbances in an unbounded Couette flow. We obtain explicit formulae for all three components of a Kelvin mode in terms of elementary functions. We then prove that Kelvin modes with parallel (though time-dependent) wave vectors can be superposed to construct the most general plane transverse shearing wave. An explicit solution is given, with any specified initial orientation, profile and polarization structure, with either unbounded or shear-periodic boundary conditions.
Description: Open Access
ISSN: 2190-5444 (Online)
Alternative Location:
Copyright: 2017 The authors published with open access at springerlink
Appears in Collections:Research Papers (A&A)

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